It is reasonable to assume that global yields move in tandem to a certain extent, driven by a global and a local component. Are there any ways to separate the two, beyond the obvious (regress the local yield changes onto an average change across all yields)? Any pitfalls, like expected/unexpected changes, credit risk, inflation etc?
I subscribe to a theory, originally postulated by Kapitsa, Jr. in Модель роста населения Земли и экономического развития человечества, that the main predictor for the global yield component would be the population growth rate. The challenge with incorporating such variables in regression analysis is that one needs to have access to time series which span 100+ years. This data is unavailable for many countries.
Yes, there IS a global yield common component here. PCA on 2s, 5s, 10s and the long-end of yield curves would objectively describe this for you.
I agree with the earlier answer that population growth is an important factor here; but there are others. Demographics is one half of this; the other is productivity, ie the output per worker. Faster growing (for either reason) economies will tend to have higher interest rates/yields. All of this before we start to think about different inflation rates in different currencies :-)
Short answer is that yields globally ARE regionally correlated, because global growth is an important factor in all of them regionally.